On the GMAT, assume that "number of factors" = "number of distinct factors".nikhilgmat31 wrote:I think question should explicity tell that 4 distinct factors.
lets p=3
3^3 leads 3*3*3 which can have factors as - 1,3,3,3,9,27 which is not 4 which leads to Answer C.
What's say of others.
np - prime numbers
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We may recall that when we add one to the exponent of each unique prime of a number, and then multiply together the sums, we get the total number of factors.sairamGmat wrote:If n and p are different positive prime numbers, which of the integers n^4, p^3 and np has (have) exactly 4 positive divisors?
(A) n^4 only
(B) p^3 only
(C) np only
(D) n^4 and np
(E) p^3 and np
Thus, we see that n^4 has 4 + 1 = 5 factors and p^3 has 3 + 1 = 4 factors.
Since n x p = n^1 x p^1, so that product has (1 + 1)(1 + 1) = 4 factors.
Answer: E
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